Nonuniform grids for Brillouin zone integration and interpolation

We present two developments for the numerical integration of a function over Brillouin zone. First, we introduce nonuniform grid, which refer to as Farey that generalizes regular grids. Second, symmetry-adapted Voronoi tessellation, general technique assign weights points in an arbitrary grid. Combining these developments, propose strategy perform zone and interpolation provides significant computational advantage compared usual approach based on uniform demonstrate our methodology context first principles calculations with study Kohn anomalies phonon dispersions graphene MgB2, evaluation electron-phonon driven renormalization band gaps diamond bismuthene. In calculations, find speedups by factor 3 4 when using density functional perturbation theory, 6 7 finite differences conjunction supercells. As result, expense between theory becomes comparable. For coupling even larger speedups. Finally, also grid can be expressed combination widely used grids, should facilitate adoption this methodology.